Viscous Scalar Conservation Law with Nonlinear Flux Feedback and Global Attractors

In this paper we study the forced viscous scalar conservation law on 0, 1.with the nonlinear flux feedback at the boundary. Global existence and uniqueness are established for L` bounded initial conditions and forcing functions. Under an appropriate growth condition on the flux function and nonlinear dissipation at the boundary, we show the existence of an absorbing set that absorbs the whole space L` 0, 1., and the existence of a compact global attractor in the L` topology.